saddle(boot)
saddle()所属R语言包：boot
Saddlepoint Approximations for Bootstrap Statistics
鞍点近似的Bootstrap统计
译者：生物统计家园网 机器人LoveR
描述----------Description----------
This function calculates a saddlepoint approximation to the distribution of a linear combination of W at a particular point u, where W is a vector of random variables. The distribution of W may be multinomial (default), Poisson or binary. Other distributions are possible also if the adjusted cumulant generating function and its second derivative are given. Conditional saddlepoint approximations to the distribution of one linear combination given the values of other linear combinations of W can be calculated for W having binary or Poisson distributions.
此功能分布在一个特定的点u，其中W是一个随机变量的向量的线性组合的W计算鞍点逼近。 W的分布可能是多项式（默认），泊松或二进制。其他分派是可能的，如果调整后的累积发电功能和它的第二个衍生。有条件的鞍点近似W的线性组合的价值，一个线性组合的分布可以计算为W二进制或泊松分布。
用法----------Usage----------
saddle(A = NULL, u = NULL, wdist = "m", type = "simp", d = NULL,
d1 = 1, init = rep(0.1, d), mu = rep(0.5, n), LR = FALSE,
strata = NULL, K.adj = NULL, K2 = NULL)
参数----------Arguments----------
参数：A
A vector or matrix of known coefficients of the linear combinations of W. It is a required argument unless K.adj and K2 are supplied, in which case it is ignored.
一个向量或矩阵W。它的线性组合系数是一个必需的参数，除非K.adj和K2提供的，在这种情况下，它会被忽略。
参数：u
The value at which it is desired to calculate the saddlepoint approximation to the distribution of the linear combination of W. It is a required argument unless K.adj and K2 are supplied, in which case it is ignored.
它需要计算W的线性组合分布的鞍点逼近，这是一个必需的参数的值，除非K.adj和K2提供的，在这种情况下，它会被忽略。
参数：wdist
The distribution of W. This can be one of "m" (multinomial), "p" (Poisson), "b" (binary) or "o" (other). If K.adj and K2 are given wdist is set to "o".
分布W，这可以是一个"m"（多项），"p"（泊松分布），"b"（二进制）或"o"（其他）。如果K.adj和K2给wdist设置为"o"。
参数：type
The type of saddlepoint approximation. Possible types are "simp" for simple saddlepoint and "cond" for the conditional saddlepoint. When wdist is "o" or "m", type is automatically set to "simp", which is the only type of saddlepoint currently implemented for those distributions.
鞍点近似的类型。可能的类型"simp"简单的鞍"cond"条件鞍点。当wdist是"o"或"m"，type"simp"，这是目前唯一的类型对于那些分布实施的鞍自动设置。
参数：d
This specifies the dimension of the whole statistic. This argument is required only when wdist = "o" and defaults to 1 if not supplied in that case. For other distributions it is set to ncol(A).
这指定维度的整体统计。此参数是必需的，只有当wdist = "o"“默认为1，如果在这种情况下不提供。对于其他发行版，它被设置为ncol(A)。
参数：d1
When type is "cond" this is the dimension of the statistic of interest which must be less than length(u). Then the saddlepoint approximation to the conditional distribution of the first d1 linear combinations given the values of the remaining combinations is found. Conditional distribution function approximations can only be found if the value of d1 is 1.
当type是"cond"这是利益的统计尺寸必须比length(u)少。然后发现第一d1其余组合值的线性组合的条件分布的鞍点逼近。条件分布函数逼近只能发现如果d1的值1。
参数：init
Used if wdist is either "m" or "o", this gives initial values to nlmin which is used to solve the saddlepoint equation.
如果wdist是使用或者"m"或"o"，这给了这是用来解决鞍点方程nlmin初始值。
参数：mu
The values of the parameters of the distribution of W when wdist is "m", "p" "b". mu must be of the same length as W (i.e. nrow(A)). The default is that all values of mu are equal and so the elements of W are identically distributed.
W的分布参数的值时wdist是"m"，"p""b"。 mu必须是相同长度的宽（即nrow(A)）。默认是mu所有值都是平等的，所以W的元素分布。
参数：LR
If TRUE then the Lugananni-Rice approximation to the cdf is used, otherwise the approximation used is based on Barndorff-Nielsen's r*.
如果TRUE然后Lugananni稻逼近民防部队使用，否则使用近似的基础上Barndorff尼尔森的R *。
参数：strata
The strata for stratified data.
地层分层数据。
参数：K.adj
The adjusted cumulant generating function used when wdist is "o". This is a function of a single parameter, zeta, which calculates K(zeta)-u%*%zeta, where K(zeta) is the cumulant generating function of W.
调整后的累积生成函数使用时wdist是"o"。这是一个参数，zeta，计算K(zeta)-u%*%zeta，其中K(zeta)是累积生成函数W·功能
参数：K2
This is a function of a single parameter zeta which returns the matrix of second derivatives of K(zeta) for use when wdist is "o". If K.adj is given then this must be given also. It is called only once with the calculated solution to the saddlepoint equation being passed as the argument. This argument is ignored if K.adj is not supplied.
这是一个参数zeta返回使用二阶导数矩阵K(zeta)时wdist是"o"功能。 K.adj如果那么这个也必须给予。它被称为只有一次被作为参数传递到鞍点方程的计算解决方案。 K.adj如果没有提供此参数将被忽略。
Details
详情----------Details----------
If wdist is "o" or "m", the saddlepoint equations are solved using nlmin to minimize K.adj with respect to its parameter zeta. For the Poisson and binary cases, a generalized linear model is fitted such that the parameter estimates solve the saddlepoint equations. The response variable 'y' for the glm must satisfy the equation t(A)%*%y = u (t() being the transpose function). Such a vector can be found as a feasible solution to a linear programming problem. This is done by a call to simplex. The covariate matrix for the glm is given by A.
如果wdist是"o"或"m"使用nlmin，以尽量减少K.adj尊重其参数zeta，鞍点方程解决。广义线性模型的泊松和二进制情况下，安装等参数的估计，解决了鞍点方程。响应变量“Y”glm必须满足方程t(A)%*%y = u（t()移调功能）。可以发现这样一个向量，线性规划问题的一个可行的解决方案。这样做是由simplex调用。的glm协矩阵给A。
值----------Value----------
A list consisting of the following components
以下组件组成的列表
参数：spa
The saddlepoint approximations. The first value is the density approximation and the second value is the distribution function approximation.
鞍点近似。首先看重的是密度近似和第二个值是分布函数逼近。
参数：zeta.hat
The solution to the saddlepoint equation. For the conditional saddlepoint this is the solution to the saddlepoint equation for the numerator.
鞍点方程的解决方案。为条件鞍，这是解决鞍点方程的分子。
参数：zeta2.hat
If type is "cond" this is the solution to the saddlepoint equation for the denominator. This component is not returned for any other value of type.
如果type是"cond"这是解决鞍点方程的分母。这个组件不会返回任何其他值type。
参考文献----------References----------
saddlepoint approximations in generalized linear models. Biometrika, 77, 787–796.
approximations to resampling distributions. Computing Science and Statistics; Proceedings of the 28th Symposium on the Interface, 248–253.
Bootstrap Methods and their Application. Cambridge University Press.
参见----------See Also----------
saddle.distn, simplex
saddle.distn，simplex
举例----------Examples----------
# To evaluate the bootstrap distribution of the mean failure time of [平均故障间隔时间，以评估引导分布]
# air-conditioning equipment at 80 hours[在80小时内的空气调节设备]
saddle(A = aircondit$hours/12, u = 80)
# Alternatively this can be done using a conditional poisson[另外，这是可以做到使用条件泊松]
saddle(A = cbind(aircondit$hours/12,1), u = c(80, 12),
wdist = "p", type = "cond")
# To use the Lugananni-Rice approximation to this[使用Lugananni水稻逼近]
saddle(A = cbind(aircondit$hours/12,1), u = c(80, 12),
wdist = "p", type = "cond",
LR = TRUE)
# Example 9.16 of Davison and Hinkley (1997) calculates saddlepoint [例如，戴维森和欣克利（1997）9.16计算鞍]
# approximations to the distribution of the ratio statistic for the[近似分布的比例统计]
# city data. Since the statistic is not in itself a linear combination[城市数据。由于统计本身并不是一个线性组合]
# of random Variables, its distribution cannot be found directly. [随机变量，其分布不能被直接发现。]
# Instead the statistic is expressed as the solution to a linear [相反，统计作为解决线性表示]
# estimating equation and hence its distribution can be found. We[估计方程，并因此可以发现其分布。我们]
# get the saddlepoint approximation to the pdf and cdf evaluated at[得到的鞍点逼近评估在PDF和CDF]
# t = 1.25 as follows.[T = 1.25如下。]
jacobian <- function(dat,t,zeta)
{
p <- exp(zeta*(dat$x-t*dat$u))
abs(sum(dat$u*p)/sum(p))
}
city.sp1 <- saddle(A = city$x-1.25*city$u, u = 0)
city.sp1$spa[1] <- jacobian(city, 1.25, city.sp1$zeta.hat) * city.sp1$spa[1]
city.sp1
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
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发表于 2012-2-16 21:43:19
